Find the positive solution of the equation. 8x^((3)/(2))+25=4121 Answer:

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Find the positive solution of the equation.  8x^((3)/(2))+25=4121 Answer:

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Subtract 25: Subtract 25 from both sides of the equation to isolate the term with the variable. $8x^{\frac{3}{2}} + 25 - 25 = 4121 - 25$Calculate result: Calculate the result of the subtraction on the right side of the equation. $8x^{\frac{3}{2}} = 4096$Divide by 8: Divide both sides of the equation by 8 to solve for $x^{\frac{3}{2}}$. $\frac{8x^{\frac{3}{2}}}{8} = \frac{4096}{8}$Calculate result: Calculate the result of the division on the right side of the equation. $x^{\frac{3}{2}} = 512$Recognize power: Recognize that 512 is a power of 2, specifically $2^9$. $512 = 2^9$Write equation: Write the equation with $x^{\frac{3}{2}}$ as $2^9$. $x^{\frac{3}{2}} = 2^9$Raise to power: To solve for x, we need to raise both sides of the equation to the power of $\frac{2}{3}$ because $\left(\frac{3}{2}\right) \cdot \left(\frac{2}{3}\right) = 1$. $x = (2^9)^{\frac{2}{3}}$Simplify exponent: Simplify the exponent on the right side by multiplying the exponents. $x = 2^{9 \cdot \frac{2}{3}}$Calculate exponent: Calculate the exponent on the right side. $x = 2^6$Recognize value: Recognize that $2^6$ is equal to 64. $x = 64$

Find the positive solution of the equation. $\newline$ $8 x^{\frac{3}{2}}+25=4121$ $\newline$ Answer:

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Find the positive solution of the equation. $\newline$ $8 x^{\frac{3}{2}}+25=4121$ $\newline$ Answer: